1. Field of the Invention
The invention relates to a velocity sensor and a semiconductor exposing apparatus in which such a velocity sensor is used as velocity detecting means in a mechanism such as an XY stage for mechanically and super-accurately positioning a sample.
2. Related Background Art
FIG. 6 is a schematic constructional view showing an example of conventional velocity detecting means of an XY stage of a semiconductor exposing apparatus.
The velocity detecting means is used to position an XY stage 14 which is guided by a movable X guide 12 and a fixed Y guide 13 and is moved on a fixed board 11 in the directions of X and Y axes shown in the drawing. The velocity detecting means comprises: a square mirror 21 provided on the XY stage 14; an X-axis laser interferometer to measure the position of the XY stage 14 in the direction of the X axis shown in the diagram; and a Y-axis laser interferometer to measure the position of the XY stage 14 in the direction of the Y axis shown in the drawing.
The X-axis laser interferometer comprises: a first laser light source 31 to emit a laser beam; a first bender 32 to change the progressing direction of the laser beam emitted from the first laser light source 31 to the X-axis direction shown in the drawing; a first polarizing beam splitter 33 to arrange the polarizing direction of the laser beam emitted from the first bender 32; and a first light amount sensor 34 to receive reflected light of the laser beam reflected by the square mirror 21. That is, the laser beam emitted from the first polarizing beam splitter 33 is reflected by the square mirror 21, after that, the reflected light again passes through the first polarizing beam splitter 33 and is received by the first light amount sensor 34. The Y-axis laser interferometer comprises: a second laser light source 41 to emit a laser beam; a second bender 42 to change the progressing direction of the laser beam emitted from the second laser light source 41 to the Y-axis direction shown in the drawing; a second polarizing beam splitter 43 to arrange the polarizing direction of the laser beam emitted from the second bender 42; and a second light amount sensor 44 to receive the reflected light of the laser beam reflected at the square mirror 21. That is, the laser beam emitted from the second polarizing beam splitter 43 is reflected by the square mirror 21, after that, the reflected light passes through the second polarizing beam splitter 43 and is received by the second light amount sensor 44. A first actuator (not shown) to generate a thrust to the fixed Y guide 13 is attached to the movable X guide 12. A second actuator (not shown) to generate a thrust to the movable X guide 12 is attached to the XY stage 14. Air slides (not shown) are provided between the movable X guide 12 and the fixed Y guide, between the movable X guide 12 and the fixed board 11, between the movable X guide 12 and the XY stage 14, and between the XY stage 14 and the fixed board 11, respectively.
The positions of the XY stage 14 in the X-axis and Y-axis directions shown in the drawing are measured by the X-axis laser interferometer and the Y-axis laser interferometer and the servo is applied to the first and second actuators, thereby positioning the XY stage 14. In this instance, in order to stabilize the servo system to reduce the positioning time, the first and second actuators generate resistance forces which are proportional to the velocity in the X-axis and Y-axis directions shown in the drawing. Therefore, the values of the necessary velocity in the X-axis and Y-axis directions shown in the drawing are obtained by calculating a difference between the position data of the XY stage 14 which are obtained by the X-axis and Y-axis laser interferometers.
However, the above conventional velocity detecting means has the following two problems.
(1) It is difficult to detect the velocity in a low velocity range before completion of the positioning operation. That is, in the semiconductor exposing apparatus, the positioning is ordinarily executed so as to obtain plus or minus (.+-.) one resolution of the X-axis and Y-axis laser interferometers. A difference between the position data of the X-axis and Y-axis laser interferometers is calculated and a servo applying period of time is ordinarily set to 1 msec or less. Therefore, in a region where the positional deviation before completion of the positioning is within a range of plus or minus (.+-.) a few resolutions, there is hardly a change in position for 1 msec. Therefore, in this region, the velocity feedback is not substantially performed. To stabilize the servo system, the gain cannot help dropping. Consequently, the time which is required for positioning increases or the accuracy against a disturbance deteriorates.
(2) Another vibrating mode (mainly, a rotating mode) is excited. That is, in the XY stage 14, several springs due to the compression properties of the air slides exist between the first and second actuators and the square mirror 21. For instance, the movable X guide 12 restricts the motions in the Y-axis and Z-axis directions shown in the drawing. Since the motions in the Y-axis and Z-axis directions shown in the drawing are restricted by air pressures, they are restricted by the compression properties of the air through the springs. Therefore, a rotating mode occurs. When a damping is applied by a velocity feedback in the X-axis direction shown in the drawing and the velocity feedback gain is raised, the rotating mode is excited. Therefore, the velocity feedback gain cannot sufficiently be increased. Eventually, a control frequency of the rigid mode cannot be sufficiently increased as well.
As one of the means for solving the above problems, there is known a method in, which when the velocity sensor fixed to an object to be measured has a relative velocity for an ambient fluid, a frictional force which occurs between the object and the fluid and is proportional to the relative velocity for the fluid is detected, thereby detecting the velocity of the object to be measured. However, even in this method, when the object to be measured moves at a super-low velocity, the frictional force that is detected by the velocity sensor is extremely small. There is a problem such that in a case having a velocity sensor of a size which is equal to or larger than about a few millimeters (mm), the above frictional force cannot be accurately detected. That is, a frictional force F.sub.1 due to an interaction with the fluid is expressed as follows. EQU F.sub.1 =k.sub.1 .times..mu..times.U/L.times.d.times.d (1)
where, k.sub.1 : proportional constant
.mu.: coefficient of friction PA0 U: relative velocity for the fluid PA0 L: thickness of laminar flow boundary layer PA0 d: dimensions of element of the velocity sensor which causes friction together with the fluid PA0 L: thickness of laminar flow boundary layer PA0 .mu.: coefficient of friction with the fluid PA0 k.sub.1, k.sub.2 : proportional constants PA0 .rho.: density of fluid PA0 k.sub.1, k.sub.2 : proportional constants.
On the other hand, a frictional force F.sub.2 which is subjected to the element of the velocity sensor that causes friction together with the fluid from a peripheral supporting portion (mainly, a bearing portion) is expressed as follows because it is proportional to the volume of the element. EQU F.sub.2 =k.sub.2 .times.d.times.d.times.d (2)
where, k.sub.2 : proportional constant
Therefore, the frictional force F.sub.1 due to the interaction with the fluid is proportional to the square of the dimensions d of the element of the velocity sensor. On the other hand, the frictional force F.sub.2 which is subjected from the peripheral supporting portion is proportional to the cube of the dimension d of the element of the velocity sensor. Therefore, in a case having the velocity sensor of a size which is equal to or larger than about a few millimeters (mm), the frictional force F.sub.2 which is subjected from the peripheral supporting portion is sufficiently larger than the frictional force F.sub.1 due to the interaction with the fluid. Therefore, the frictional force F.sub.1 due to the interaction with the fluid cannot be detected.